Lines crossing a tetrahedron and the Bloch group

  • Kevin Hutchinson

    University College Dublin, Ireland
  • Masha Vlasenko

    Trinity College, Dublin, Ireland
Lines crossing a tetrahedron and the Bloch group cover

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According to B. Totaro (Milnor K-theory is the simplest part of algebraic K-theory, K-theory 6 (1992), 177–189), there is a hope that the Chow groups of a field can be computed using a very small class of affine algebraic varieties (linear spaces in the right coordinates), whereas the current definition uses essentially all algebraic cycles in affine space. In this note we consider a simple modification of using only linear subvarieties in affine spaces and show that it maps surjectively to the Bloch group for any infinite field . We also describe the kernel of this map.